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An explosion in linear algebra

rwells
4-Participant

An explosion in linear algebra

Regarding the graphing in 3D space on mathcad professional 2000 and not having internet access, I knew that the dialouge on this site would be moderated and vernacular to only the most advanced engineering scientists. The lines I had attempted (usually only two or three of them) always looked like one squigly line inside the box. I could not convince myself that each data point touched the coordinates I was "expecting" tw see, and I certainly did not "see" two lines intersecting in space. And then I re-opened an old worksheet and began using the tilt, rotate, and twist commands in the format graph box. The graph began to look like the two lines that I was expecting, and it became also evident that the where all accurate. It was simply the case that one of the lines may have been oriented in such a way that it was jumping out of the screen toward me at an awward angle. The breakthrough occured at my realization that the box can be oriented so the the two lines not only "look" as linear as possible (like they would on a flat page) but they are indeed mathematicly linear. They will then only differ in length. And confusion that seprates the vector from the function is that the vector needs more instruction than a f(x) = y type function.

If I where holding a box with 3 bullet holes that where shot right down through the sides and then exited the bottom of the box, the two lines where now visualized as tragectorys of the bullet path. by simply multiplying one the lines by its multiplicative inverse I could now shoot one of the bullets on through the bottom of the box, and have that line show up as extending as a dotted line.

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